I'm going to speak in defense of the seemingly ridiculous rules rescues have, and this is from someone who has bought a puppy, having failed to find a suitable rescue) and also rescued multiple times (even from abroad).
Rescues are DESPERATE to not have a dog returned to them, for lots of reasons but mostly because it is a terrible and damaging thing for the dog to be passed from pillar to post. they know full well the factors that contribute to an adoption breaking down, they know full well that their dogs need dedicated, knowledgeable people who can be prudent about the challenges that will, inevitably, be faced in the first months (sometimes years) and that is why they have their rules.
many many years ago we adopted a rescue, our kids were dog savvy 5 ish and 7 ish. we were experienced owners. it was hard, really really hard, to divide my precious time between the children and the dog, he was a chewer, the kids toys and shoes got destroyed (easy to say keep them out the way, harder to actually do with small kids). he was boisterous, the kids were regularly knocked over. he pulled on walks, it was very difficult to walk the kids and him together, but the kids were too small to leave at home while i taught him how to walk nicely and recall successfully. these are just the tip of the iceberg of the challenges of having a (any) dog and children, as anyone who has done both knows. but OBVIOUSLY, a lot of people, would quickly get sick of living this way, and return the dog to the rescue. and that is why they have the rules about children. they know that people's tolerance for poor behavior and ability to dedicate time to training is limited when you have children. and it's much "easier" to hand back a rescue than it is a £2000 cute puppy you've paid for.
Our local FB page is FULL of lost and found dogs, practically every day, low fences and nervous unsettled dogs do not mix. some lost for weeks on end. a few have been killed on the roads,
Introducing a new dog to an existing pet can be a laborious and difficult process, and might never result in an easy, happy relaxed relationship between them, you just don't know, another key reason why adoptions can fail
i could go on but this is long
you have to see their point, frustrating though it is - they are working in the best interests of the dog, and they have seen it all 1000 times before, it is coming from a place of knowledge and experience.